How do you determine ERP and EIRP Values for a RF Transmitting System?

Publication Number: 412172	Rule Parts:	Publication Date: 08/07/2015
Keyword: Guidance Determining ERP and EIRP

---

First Category:	Equipment Authorization Process *
Second Category:	General [Equipment Authorization Process]

---

Question:   How do you determine ERP and EIRP Values for a RF Transmitting System?

---

Answer:   The attached document 412172 D01 Determining ERP and EIRP v01r01provides methods for determining the Effective Radiated Power (ERP) and Equivalent Isotropically Radiated Power (EIRP) of a RF Transmitting System. Also, see ANSI C63.10-2013, Annex G.

Attachment List:

412172 D01 Determining ERP and EIRP v01r01
WebSite:https://apps.fcc.gov/kdb/GetAttachment.html?id=fzlsGm%2Fe68Ymx58IAmzNbw%3D%3D&desc=412172%20D01%20Determining%20ERP%20and%20EIRP%20v01r01&tracking_number=47469

GUIDELINES FOR DETERMINING THE EFFECTIVE RADIATED POWER (ERP)AND EQUIVALENT ISOTROPICALLY RADIATED POWER (EIRP) OF AN RFTRANSMITTING SYSTEM

1. IntroductionMany FCC rule parts specify power and/or emission limits in terms of the transmitter system (transmitter,radiating antenna, and cable connector) effective radiated power (ERP) or equivalent (or effective)isotropically radiated power (EIRP).These guidelines are intended to demonstrate how to determine the EIRP or ERP from the results of apower measurement performed under far-field conditions with respect to all transmit and receive(measurement) antennas.EIRP and ERP are similarly defined as the product of the power supplied to the antenna and the antennagain (when the power and gain are represented in linear terms). The primary difference is that for ERPthe antenna gain is expressed relative to an ideal half-wave dipole antenna, whereas with EIRP theantenna gain is expressed relative to an ideal (theoretical) isotropic antenna. EIRP and ERP can beexpressed mathematically as described in the following sections.

1.1. Field Strength Approach (linear terms):

eirp = pt x gt = (E x d)2/30                                                              (1)

where:

pt = transmitter output power in watts,

gt = numeric gain of the transmitting antenna (unitless),

E = electric field strength in V/m,

d = measurement distance in meters (m).

erp = eirp/1.64 = (E x d)2/(30 x 1.64)                                           (2)

where all terms are as previously defined.

1.2. Power Approach (logarithmic terms):

ERP or EIRP = PT + GT – LC                                                              (3)

where;

ERP or EIRP = effective radiated power or equivalent isotropically radiated power(expressed in the same units as PT, typically dBW, dBm, or power spectral density(PSD)2), relative to either a dipole antenna (ERP) or an isotropic antenna (EIRP);

PT = transmitter output power, expressed in dBW, dBm, or PSD;

GT = gain of the transmitting antenna, in dBd (ERP) or dBi (EIRP);

LC = signal attenuation in the connecting cable between the transmitter and antenna, in dB.3

1.3. Relationship Between ERP and EIRP:

The numeric gain of an ideal half-wave dipole antenna is 1.64 and the numeric gain of an idealisotropic antenna is 1.0.

The gain of an ideal half-wave dipole antenna relative to an ideal isotropic antenna is 10log1.64or 2.15 dBi.

Therefore, if the antenna gain in dBd is unknown, it can be determined from the gain in dBi viathe following relationship:

GT(dBd) = GT(dBi) - 2.15 dB.                                                                 (4)

Alternatively, the EIRP can be determined from Equation (3) and then converted to ERP based onthe maximum antenna gain relationship by applying the following equation:

ERP = EIRP – 2.15 dB.                                                                           (5)

Similarly, the EIRP can be determined from the ERP as follows:

EIRP = ERP + 2.15 dB. (6)

2. Applications

The following paragraphs discuss the appropriate methods for applying the equations presented abovedepending on the power measurement configuration used.

2.1. DUT power measured in a conducted test configuration

When the DUT power is measured using a direct connection between the transmitter antenna portand the measurement instrumentation via a coaxial cable (conducted test), and the transmitantenna gain is a known quantity, then the ERP and/or EIRP can be calculated by directapplication of Equation (3) and using the relationships defined in Equations (4), (5), or (6), asappropriate.The value to be used for PT in these equations is the measured power level (in dBm, dBW orPSD), adjusted to account for external test peripherals (cable loss, external attenuation, and/orexternal amplification).The value to be used for GT is the gain associated with the DUT transmit antenna, expressed ineither dBd (ERP) or dBi (EIRP). Typically, the maximum rated antenna gain is used indetermining the maximum ERP or EIRP levels at or near the fundamental frequency; however,this practice can lead to conservative (i.e., overestimated) values when applied to spuriousemissions on frequencies that are well removed from the frequency range over which the transmitantenna is presumed to have been optimized.The value used for GT may require some adjustment for devices that utilize multiple transmitantennas (e.g., MIMO) and/or beam forming or beam steering (e.g., Smart Antenna)technologies. In such configurations, an adjustment to the transmit antenna gain used incalculating the ERP or EIRP may be required. For additional guidance on determining andapplying this adjustment factor, refer to clauses 13 and 14 in ANSI C63.10-2013 and FCCguidance provided in KDB Publication 662911.

2.2. Direct calculation from the DUT power measured in a radiated test configuration (i.e.,signal/antenna substitution techniques not used).When the DUT power is measured using a radiated test configuration, the EIRP can bemathematically approximated using the power (logarithmic) approach as follows:

EIRP = PR + LP (7)

where;

EIRP = equivalent (or effective) isotropically radiated power (in same units as PR);
PR = adjusted received power level, in dBW, dBm, or PSD;
LP = basic free space propagation path loss, in dB.

The received power level PR is the measured power adjusted for measurement antenna gain,connecting cable loss, and any external signal amplification or attenuation used in the testconfiguration. Mathematically:

PR = PMeas – GR + LC + LAtten - GAmp                                                                   (8)

where;

PMeasured = measured power level, in dBW, dBm or psd;
GR = gain of the receive (measurement) antenna, in dBi;
LC = signal loss in the measurement cable, in dB;
LAtten = value of external attenuation (if used), in dB;
GAmp = value of external amplification (if used), in dB.
The free space propagation path loss LP is determined from the following equation:

LP = 20 Log F + 20 Log D – 27.5                                                                                  (9)

where:
LP = basic free space propagation path loss, in dB;
F = center frequency of radiated DUT signal, in MHz;
D = measurement distance, in meters.The ERP can then be determined from the EIRP by applying Equation (5).

When the DUT power is measured using a radiated test configuration, the eirp can be directlydetermined using the field strength (linear) approach by applying Equation (1).

The erp can then be determined from the eirp by applying Equation (2).

2.3. DUT power measured in a radiated test configuration using signal/antenna substitution techniques.
The ERP/EIRP can be determined from the power setting of a signal generator used in thesignal/antenna substitution test configuration as follows:

ERP or EIRP = PSigGen + GT - LC                                             (10)

where:

PSigGen = power setting of the signal generator that produces the same received powerreading as the DUT, in dBm, dBW or psd;
GT = gain of the substitute antenna, in dBd (ERP) or dBi (EIRP);
LC = signal loss in the cable connecting the signal generator to the substitute antenna, indB.Change Notice08/07/2015: 412172 D01 Determining ERP and EIRP v01r01 replaces 412172 D01 Determining ERP and EIRPv01. Changes made to discuss far field measurements, spurious emissions, reference to ANSI C63.10-2013 andeditorial edits

Change Notice 08/07/2015: 412172 D01 Determining ERP and EIRP v01r01 replaces 412172 D01 Determining ERP and EIRPv01. Changes made to discuss far field measurements, spurious emissions, reference to ANSI C63.10-2013 andeditorial edits.

Website: https://apps.fcc.gov/kdb/GetAttachment.html?id=fzlsGm%2Fe68Ymx58IAmzNbw%3D%3D&desc=412172%20D01%20Determining%20ERP%20and%20EIRP%20v01r01&tracking_number=47469